Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.00$, and bags of cookies cost $$3.50$, and sales equaled $$47.50$ in total. There were $7$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8x+3.5y = 47.5}$ ${y = x+7}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+7}$ for $y$ in the first equation. ${8x + 3.5}{(x+7)}{= 47.5}$ Simplify and solve for $x$ $ 8x+3.5x + 24.5 = 47.5 $ $ 11.5x+24.5 = 47.5 $ $ 11.5x = 23 $ $ x = \dfrac{23}{11.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+7}$ to find $y$ ${y = }{(2)}{ + 7}$ ${y = 9}$ You can also plug ${x = 2}$ into $ {8x+3.5y = 47.5}$ and get the same answer for $y$ ${8}{(2)}{ + 3.5y = 47.5}$ ${y = 9}$ $2$ bags of candy and $9$ bags of cookies were sold.